Question

Find the area of sector of a circle with radius $4cm$ and angle ${30}^o$. Find the area of corresponding major sector, $(\pi =3.14)$

Answer 1

We have,

Let the radius of circle $r=4cm.$

Angle $\theta ={30}^o$

Area of sector of circle

$=\frac{\theta }{{360}^o}\times \pi r^2$

$=\frac{{30}^o}{{360}^o}\times \pi \times 4\times 4$

$=\frac{\pi }{12}\times 16$

$=\frac{4\pi }{3}$

$=\frac{4}{3}\times 3.14$

$=4.186c{m}^2$

Area of major sector = Area of circle-area of minor sector

$=\pi r^2-4.186$

$=3.14\times 4\times 4-4.186$

$=3.14\times 16-4.186$

$=50.24cm{.}^2$

Hence, this is the answer.